Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define mp make_pair
#define pb push_back
#define fi first
#define se second
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,int> pli;
const int inf=1e9;
const ll Inf=1e18;
const int N=2e5+10;
const int mod=0;
int gi() {
    int x=0,o=1;char ch=getchar();
    while((ch<'0'||ch>'9')&&ch!='-') ch=getchar();
    if(ch=='-') o=-1,ch=getchar();
    while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
    return x*o;
}
template<typename T> bool chkmax(T &a,T b) { return a<b?a=b,1:0; };
template<typename T> bool chkmin(T &a,T b) { return a>b?a=b,1:0; };
int add(int a,int b) { return a+b>=mod?a+b-mod:a+b; }
int sub(int a,int b) { return a-b<0?a-b+mod:a-b; }
void inc(int &a,int b) { a=(a+b>=mod?a+b-mod:a+b); }
void dec(int &a,int b) { a=(a-b<0?a-b+mod:a-b); }
int n,q[N],t[N],f[N];
int main() {
    cin>>n;
    for(int i=1;i<=n;i++) q[gi()]=i;
    for(int i=n-1;i;i--) {
        if(!t[i+1]) {
            if(q[i]>q[i+1]) t[i]=1,f[i]=i+1;
        }
        else {
            if((q[f[i+1]]<q[i])+(q[i]<q[i+1])+(q[i+1]<q[f[i+1]])==2) t[i]=t[i+1],f[i]=f[i+1];
            else t[i]=t[i+1]+1,f[i]=i+1;
        }
    }
    printf("%d\n",t[1]);
    return 0;
}